Complete each section to show your understanding for linear patterns.
The following tables represent linear patterns. The tables and graphs are created using Desmos.com.
- Find the missing values in each table. Table 1: (3, 7) and (12,15); Table 2: (4, 9) and (21, -42); Table 3: (-2, 4) and (8, 24)
- Graph each table on a coordinate plane.
- Calculate the slope using the table. Table 1: change in \(y\) is 4 and change in \(x\) is 1, i.e. slope is 4; Table 2: change in \(y\) is -3 and change in \(x\) is 1, i.e. slope is -3; Table 3: change in \(y\) is 2 and change in \(x\) is 1, i.e. slope is 2.
- Calculate the slope using the graph.
- Determine the point of the \(y\) intercept. Table 1: (0,-5) , Table 2: (0,18), Table 3: (0,8) .
- Write an equation to determine the \(y\)–value given any \(x\)-value. Table 1 equation: \(y = 4x -5\); Table 2 equation: \(y=21 – 3x\); Table 3 equation: \(y= 2x + 8\)
Given the growth pattern shown in Figure 2 and Figure 4.
- Draw Figure 3. Figure 3 has 3 rows of 6, so a row of 6 is added to figure2.
- Explain the growth pattern. 6 is added each time.
- Determine the number of squares in Figure 0. Figure 0 has 1 square.
- Write the equation to represent the number of squares for any figure. 1 + 6n, where n is the figure number.
- Using the context of growth patterns, explain why \(m\) represents the slope and \(b\) represents the \(y\)-intercept in the slope-intercept formula \(y=mx+b\). The slope is 6 since, 6 squares is added each time and 1 is figure 0, so the \(y\)-intercept
A given linear pattern has 10 squares in Step 3. The pattern grows by -4 squares every 2 steps.
- Create a table for this pattern.
- Calculate the slope to represent the growth for this pattern. Slope is -4
- Calculate the equation to calculate the number of squares for each step. \(y = 22 – 4x\)